This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions.
Volume 16 article 546 pages: 404 - 409
The prerequisites for reducing the test sample chi-square Pearson test size from 400 to 32 or fewer examples while maintaining its power are considered. The urgency of the problem results from the fact that when learning and testing the biometric identification means to identify the personality, it is not possible to use large volumes of learning and test samples. The conditions under which the chi-square test on small samples from the continuous distribution of values becomes a discrete distribution of values are formalized. Normal and uniform laws of values distribution use histograms with uniform intervals, which accurately relate the central intervals of the histogram to the mathematical expectation calculated on the test sample. 16 experiments shown that the chi-square-synchronized test built on histograms with four equal intervals has a discrete probability spectrum consisting of only 20 significant spectral lines. A simple method for estimating the informativity of each of the important spectral components is proposed. Traditional statistical assessments can be strengthened by the following deeper level of the spectral components analysis of small samples of biometric data. The second deeper level of statistical processing should be substantially more powerful. Under the same conditions, the computational informativity increases from 2.22 bits to 24.95 bits due to the transition from simple continual calculations to discrete calculations of high computational complexity.
Volchikhin, V.I., Ivanov, A.I., Funtikov, V.A. (2005). Fast learning algorithms for neural network mechanisms of biometric-cryptographic information protection. Publishing House of the Penza State University, Penza.
Malygin, A.Yu., Volchikhin, V.I., Ivanov, A.I., Funtikov, V.A. (2006). Fast testing algorithms for neural network mechanisms of biometric-cryptographic information protection. Publishing House of the Penza State University, Penza.
Yazov, Yu.K. (2012). Neural network protection of personal biometric data. Radio Engineering, Moscow.
Federal Agency on Technical Regulating and Metrology. (2001). R 50.1.037-2002. Recommendations on standardization. Applied statistics. Rules for verifying the agreement between the experimental and the theoretical distributions. Part I. x2 type criteria.
Serikova, N.I., Ivanov, A.I., Kachalin, S.V. (2014). Biometric stats: smoothing histograms based on small training sample. Scientific Journal of Science and Technology, vol. 3, no. 55, 146-150.
Serikova, N.I. (2015). Assessment of the likelihood of the normal distribution hypothesis by the Gini criterion for smoothed histograms constructed on small test samples. Questions of Radio Electronics, vol. 1, 85-94.
Ivanov, A.I., Akhmetov, B.B., Serikova, Yu.I. (2016). Strengthening the power of the chi-square test with tenfold increase in freedoms of statistical computations on small test samples. Reliability and Quality of Complex Systems, vol. 4, no. 16, 121-127. DOI: 10.21685/2307-4205-2016-4-17
Akhmetov, B.B., Ivanov, A.I. (2016). Multidimensional statistics of essentially dependent biometric data generated by neural network emulators of quadratic forms. LEM, Almaty.
Akhmetov, B.B., Ivanov, A.I., Serikova, N.I., Funtikova, Yu.V. (2015). The discrete nature of the chi-square test distribution for small test samples. Bulletin of the National Academy of Sciences of the Republic of Kazakhstan, vol. 1, no. 353, 17-25.
Kulagin, V.P., Ivanov, A.I., Gazin, A.I., Akhmetov, B.B. (2016). Cyclic continuum-quantum computing: Strengthening the Chi-Square test power on small samples. Analytics, vol. 30, no. 5, 22-29.
Volchikhin, V.I., Ivanov, A.I., Serikov, A.V., Serikova, Yu.I. (2017). Quantum superposition of the state discrete spectrum of mathematical correlation molecule for small samples of biometric data. Mordovia University Bulletin, vol. 27, no. 2, 224-238. DOI: 10.15507/0236-2910.027.201702.224-238
Volchikhin, V.I., Ivanov, A.I. (2017). Neural Network Molecule: a Solution of the Inverse Biometry Problem through Software Support of Quantum Superposition on Outputs of the Network of Artificial Neurons. Mordovia University Bulletin, vol. 27, no. 4, 518-529. DOI: 10.15507/0236-2910.027.201704.518-529
Volchikhin, V.I., Ivanov, A.I., Gazin, A.I., Bannih, A.G. (2017). Conditions of obtaining the discrete kurtosis spectrum of statistical distributions of biometric data for small samples. Journal of Computational and Engineering Mathematics, vol. 4, no. 4, 53-63. DOI: 10.14529/jcem170405
Nilson, M., Chang, I. (2006). Quantum calculations and quantum information. Mir Publishers, Moscow.
Filippov, V.V., Mitsuk, S.V. (2017). Modelling magnetoresistance effect in limited anisotropic semiconductors. Chinese Physics Letters, vol. 34, no. 7, 077201. DOI: 10.1088/0256-307X/34/7/077201
Stepanov, N.F. (2001). Quantum mechanics and quantum chemistry. Mir Publishers, Moscow.
State Standard R 52633.5-2011. (2011). Data Protection. Information Protection Technique. Automatic Learning Neural Network Converters Biometry-Code Access. Standartinform, Moscow.
Ivanov, A.I. (2016). Multidimensional neural network processing of biometric data with software reproduction of quantum superposition effects. Penza Scientific and Research Electronic Technical Institute, Penza